The Czech Republic's Novak needed an 18-point service game to hold for a 2-1 lead against Vincente in delayed early action.
Games then went comfortably with serve until the eighth game when Novak broke for 5-3.
Aided by the only ace of the set, he went on to win in the next game.
The second set became more of the same.
Breaks in the seventh and ninth games were enough for Novak to book his place in the last eight and a clash with the winner of the much-delayed clash between the fourth seed and another former champion, Sjeng Schalken, of the Netherlands, and unseeded Spaniard Felix Mantilla.
That match was a victim of the almost incessant afternoon rain.
"I don't think it was too easy out there," said Novak who is looking to repeat his 1996 success and join American Tim Wilkison as the only dual winner in the past 25 years.
"The surface out there was the fastest it has been in the six years I've been coming here.
"I was pretty lucky in the first set. He had so many break-points - nine I think - in the third game. I saved all of them.
"Auckland is pretty special for me. I won my first [of four] ATP titles here. Everything is so different now. Six years ago I had nothing to lose."
Of his decision, unlike most of his rivals, to play in the doubles, the ever-friendly Novak said: "It is better to play doubles than practise."
Francisco Clavet's giantkilling run - a carry-over from last year when he went all the way to the final - ended abruptly when he was beaten 6-3, 6-3 by unseeded Argentine David Nalbandian.
At 33, Spaniard Clavet is the oldest singles player on the ATP. The disruption of three rain breaks was obviously too much for the tournament regular.
Belgian Gilles Elseneer's hopes of carrying his long run which began in the first round of qualifying last Saturday into the quarters ended on a back court.
After taking Frenchman Jerome Golmard to a first-set tiebreaker, Elseneer won only two games in the second.
Golmard's reward? A clash with either the top seed, Russian Marat Safin, or 1997 champion Swede Jonas Bjorkman, who repeatedly tried to beat the rain to get through their match late last night.
Greg Rusedski, of Britain, was another victim of the unwelcome Auckland weather.
After holding the early advantage, he dropped the first set of his court six clash with Czech Michal Tabara 5-7 but broke Tabara in the first game of the second before scuttling off for yet another prolonged rain delay.
With so much uncertainty and with a host of yet-to-be-played (or completed) games, organisers said they would have to wait until this morning before even contemplating today's schedule.
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